已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值

已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值
已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值

已知xy=8满足x²y-xy²-x+y=56,求x²+y²的值
x²y-xy²-x+y=56
xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
(8-1)(x-y)=56
x-y=8
(x-y)²=64
x²-2xy+y²=64
x²+y²=64+2xy=80

x²y-xy²-x+y
=xy(x-y)-(x-y)
=(x-y)(xy-1)
=(x-y)(8-1)
=7(x-y)
=56
x-y=56÷7=8
x²+y²
=(x-y)²+2xy
=8²+8×2
=80

x²y-xy²-x+y=56
=xy(x-y)-(x-y)=56
(xy-1)(x-y)=56
7(x-y)=56
得 x-y=8
所以
x²+y²=(x-y)²+2xy=64+16=80